Clear-headed, so bear releases American (5)
I believe the answer is:
sober
'clear-headed' is the definition.
(I've seen this before)
'so bear releases american' is the wordplay.
'releases' suggests deleting specific letters.
'american' becomes 'a' (common abbreviation - e.g. in organisation names).
'bear' with 'a' removed is 'ber'.
'so'+'ber'='SOBER'
(Other definitions for sober that I've seen before include "Serious, thoughtful" , "Serious, restrained" , "Abstemious in robes" , "not moved" , "Restrained, grave" .)